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Nov 3, 2018
11/18

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Borys, Andrzej

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300 pages : 25 cm

Topics: Echo suppression (Telecommunication), Volterra equations, Echo suppression (Telecommunication),...

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Jun 20, 2019
06/19

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Gripenberg, G. (Gustaf)

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xxii, 701 p. : 24 cm

Topics: Functional equations, Integral equations, Volterra equations

Equivalent impedance of a rough surface is determined by solving the problem of radiowave propagation over rough random surface by using the parabolic equation method. We consider horizontal polarization and assume the rough surface, defined by discrete points, to be perfectly conducting. This assumption has minimum effects for frequencies in the VHF band and above. The essential point of this thesis is to solve numerically a Volterra integral equation of the second kind for the surface...

Topics: Radio wave propagation, Shortwave radio, Volterra equations, Surface roughness

Structural synthesis is the analysis of the dynamic response of a system when either subsystems are combined (substructure coupling) or modifications are made to substructures (structural modification). The integral equation formulation for structural synthesis is a method that requires only the baseline transient response, the baseline modal parameters, and the impedance of the structural modification. The integral formulation results in a Volterra integral equation of the second-kind. An...

Topics: DTIC Archive, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *INTEGRAL EQUATIONS, DYNAMIC RESPONSE,...

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were...

Topics: NASA Technical Reports Server (NTRS), NONLINEAR SYSTEMS, STOCHASTIC PROCESSES, LIE GROUPS, VOLTERRA...

Nonlinear heat flow in a heterogeneous material is considered. In this model, the internal genergy and heat flux depend upon the history of the temperature and the gradient of the temperature respectively. The heat conservation law leads to a Nonlinear Volterra integrodifferential equation with appropriate boundary conditions. This problem is solved under physically reasonable assumptions and its homogenization is investigated: introducing a small parameter beta measuring the 'tightness' of the...

Topics: DTIC Archive, Attouch,Hedy, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *Volterra...

Topics: DTIC Archive, Renardy,M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *POLYMERS, *ASYMPTOTIC...

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May 28, 2011
05/11

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NON

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This report lists reports, articles and other documents recently announced in the NASA STI Database.

Topics: NONLINEAR SYSTEMS, COEFFICIENTS, COMPUTATIONAL GRIDS, NONLINEARITY, NEURAL NETS, VOLTERRA...

In this paper the optimal control problem for integrodifferential equations of Volterra type are investigated where the targets sets are elements of some function space. The approach used is the abstract theory of Dubovitskii and Milyutin, the result is a necessary condition in form of a maximum principle.

Topics: DTIC Archive, Kappel,F, RESEARCH CENTER GRAZ (AUSTRIA), *CONTROL THEORY, DIFFERENTIAL EQUATIONS,...

The equations governing the motion of viscoelastic materials with fading memory incorporate a nonlinear elastic-type response with a natural dissipative mechanical. Our purpose is to discuss the subtle effects of this mechanism in viscoelastic materials of Boltzmann type. Recent results on the global existence and decay of classical solutions for smooth and small data (in one space dimension) are reviewed for smooth and singular memory kernels; for smooth kernels a number of such results can be...

Topics: DTIC Archive, Nohel,John A, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *EQUATIONS OF...

The effects of earthquakes on the rotational motion of the earth were studied. The connection between the fault parameters and the corresponding changes in the moments and products of inertia were analytically developed. The reciprocal theorem of elasticity and Volterra's formula were applied as well as the displacement and stress fields for the second degree static response of the earth model being used. The numerical results of the investigation yield the magnitude and direction of the pole...

Topics: NASA Technical Reports Server (NTRS), EARTH GRAVITATION, EARTH ROTATION, EARTHQUAKES, GRAVITATIONAL...

During this second three month phase of the seed project we have consolidated the phase 1 work on the Volterra formulation of linear quasistatic viscoelasticity problems, and three papers have now been submitted to research journals. Another paper is expected to be submitted before the summer. The visit of Dr. A.R. Johnson during March 1-8 was highly productive. During this time Drs. Johnson and Shaw implemented an adaptive solution procedure into Dr. Johnson's existing code for numerically...

Topics: DTIC Archive, Whiteman, J. R., BRUNEL UNIV UXBRIDGE (UNITED KINGDOM), *FINITE ELEMENT ANALYSIS,...

This research results are contained in the eleven papers published during the course of the research. Abstracts of these papers are contained in this document. Contents: Numerical Solutions to Stochastic Difference Equations; Approximate Solution of Random Differential Equations; Numerical Solution to a System of Random Volterra Integral Equations; Optimal Processes Governed by Integral Equations with Unilateral Constraint; Numerical Solution of Random Love's Integral Equation; Mixed Min-Max...

Topics: DTIC Archive, Bota, Kofi B, ATLANTA UNIV GA, *COMPUTATIONS, COEFFICIENTS, DIFFERENCE EQUATIONS,...

A general model for the nonlinear motion of a one dimensional, finite, homogeneous, viscoelastic body is developed and analysed by an energy method. It is shown that under physically reasonable conditions the nonlinear boundary, initial value problem has a unique, smooth solution (global in time), provided the given data are sufficiently 'small' and smooth, moreover, the solution and its derivatives of first and second order decay to zero as t yields infinity. Various modifications and...

Topics: DTIC Archive, Dafermos,C M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *VOLTERRA...

An efficient method of computing structural response of multi-story nonlinear base isolated buildings for a given seismic event is presented. Using a recursive block-by-block convolution (RBBIEF) solution to the governing nonlinear Volterra integral equation, structural base motion acting through an arbitrary number of nonlinear base isolators can be computed quickly and accurately. The general solution to the governing nonlinear Volterra integral is formulated and subsequently converted into...

Topics: DTIC Archive, Jarque, Al V, NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF MECHANICAL ENGINEERING,...

Topics: DTIC Archive, Berger,Marc A, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *STOCHASTIC...

Asymptotic lower bounds for the L2 norms of solutions of initial-boundary value problems associated with the equation of the title are derived for a simple case in which the equation fails to exhibit strict hyperbolicity. It is shown that in such cases the norm of a solution will be bounded away from zero as t approaches infinity even as the damping factor gamma becomes infinitely large.

Topics: DTIC Archive, Bloom,Frederick, SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS AND STATISTICS,...

Topics: DTIC Archive, Londen,Stig-Olof, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *KERNEL...

This report concerns two so-called inverse problems of mathematical physics. These are: the problem of determining a second-order differential operator (in a normal form) on the half-axis from its spectral function, and, the problem of determining a hyperbolic boundary value problem of a special form in a (non-characteristic) half-plane from its response on the boundary to a unit impulse at some reference time t=o (boundary value of the Riemann function).

Topics: DTIC Archive, Symes,W, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *BOUNDARY VALUE...

We consider the qualitative behaviour of exact and approximate solutions of integral and integro-differential equations with fading memory kernels. Over long time intervals the errors in numerical schemes may become so large that they mask some important properties of the solution. One frequently appeals to stability theory to address this weakness, but it turns out that, in some of the model equations we have considered, there remains a gap in the analysis. We consider a linear problem and we...

Topics: DTIC Archive, Edwards, John T., Ford, Neville J., Roberts, Jason A., CHESTER COLL (UNITED KINGDOM),...

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on...

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, CONTROL THEORY, LINEAR SYSTEMS, OPTIMIZATION,...

Matching conditions that optimize the third-order intermodulation distortion of small-signal MESFET amplifiers, subject to available-gain criteria, are derived. A numerical formulation of the Volterra series is used in conjunction with a complete equivalent circuit of the FET. The sensitivity of IP(3) to gamma (s) decreased with frequency and can be related to the MESFET's stability. (RRH)

Topics: DTIC Archive, Maas, Stephen A, AEROSPACE CORP EL SEGUNDO CA LAB OPERATIONS, *EQUIVALENT CIRCUITS,...

The motion of viscoelastic materials can be modelled by partial integrodifferential equations. For several model problems, recent investigations have been concerned with the question whether or not these equations allow the development of shocks. This paper is concerned with Lax-Wendroff methods for a class of hyperbolic history value problems. These problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop...

Topics: DTIC Archive, Markowich,Peter, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *BOUNDARY VALUE...

In this paper we discuss the numerical solution of a problem which arises in polymer rheology: A mathematical model was derived to describe the elastic recovery of molten plastics. We replace this model by a discrete model, for which the solution can immediately be constructed by computer. The main part of this paper concerns the relation between the solutions to the original and discretized models. The original problem is a Volterra equation; Volterra equations usually occur when one models...

Topics: DTIC Archive, Nevanlinna,Olavi, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *RHEOLOGY,...

Reduced dimension or subspace signal processing algorithms are studied for several classes of signal processing problems. The approach consists of mapping data into a subspace with a rectangular matrix transformation prior to application of the signal processing algorithm. This approach reduces computational complexity, reduces the variability associated with quantities estimated from data, and generally introduces some asymptotic performance loss. However, in situations with limited data, the...

Topics: DTIC Archive, Van Veen, Barry, WISCONSIN UNIV-MADISON, *SIGNAL PROCESSING, ALGORITHMS, MAXIMUM...

This paper presented two results: a new structure for the solution of nonlinear analytic systems, and an application of Bellman's Fundamental Technique to obtain the sub-optimal-feedback control of a class of quasilinear systems with non-quadratic performance indices. The application of the Fundamental Technique with a nonlinear auxiliary equation is shown to result in higher order approximating equations which are linear. Using the method by separation of variables, two examples are solved....

Topics: DTIC Archive, Singh,Ram-Nandan P, MASSACHUSETTS INST OF TECH CAMBRIDGE ELECTRONIC SYSTEMS LAB,...

The subject of this paper is a version of the inverse reflection problem for a smoothly stratified elastic medium. The same mathematics describes the inverse problem of the vibrating string. This problem is solved in a constructive way. Also, a priori estimates are derived which exhibit the continuous dependence of the solution (index of refraction, relative sound speed) on the data (scattering or reflection measurements). (Author)

Topics: DTIC Archive, Symes,W, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *INVERSE SCATTERING,...

We use energy methods to study global existence, boundedness, and asymptotic behavior as t approaches infinity, of solutions of the two Cauchy problems (and related initial-boundary value problems).

Topics: DTIC Archive, Dafermos,C M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *NONLINEAR...

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in experimental aeroelasticity are reviewed. These results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the Active Aeroelastic Wing (AAW) aircraft.

Topics: NASA Technical Reports Server (NTRS), VOLTERRA EQUATIONS, AEROELASTICITY, NONLINEARITY, IMPULSES,...

In this paper we survey recent results concerning global existence and decay of smooth solutions of certain quasilinear hyperbolic Volterra equations which provide models for the motion of one-dimensional viscoelastic solid of the Boltzmann type. We also sketch the derivation of these equations from physical principles, discuss the physically appropriate assumptions, and prove a special case of a new existence theorem for the Cauchy problem. (Author)

Topics: DTIC Archive, Hrusa,W J, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *Volterra equations,...

Topics: DTIC Archive, Londen,S O, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *Volterra equations,...

This study was directed at the analysis and characterization of nonlinearities associated with the AFSATCOM/ALT-32H interference problem and the development of an automatic nonlinear cancellation system. Analysis included the use of power series, volterra series, and perturbation analysis to predict the generation of intermodulation products. Characterization studies included the use of variable power input two-tone or notch noise to measure IMP generation by various nonlinear devices. Manual...

Topics: DTIC Archive, Burgess, Lawrence R, MAGNAVOX-GENERAL ATRONICS PHILADELPHIA PA, *ADAPTIVE SYSTEMS,...

A mathematical model for nonlinear heat flow in a rigid body of material with memory leads to the integrodifferential equation problem which is analyzed by an energy method developed jointly with C. M. Dafermos. Global existence, uniqueness, boundedness and the decay of smooth solutions as t approaches infinity are established for sufficiently smooth and small data, under physically reasonable assumptions.

Topics: DTIC Archive, Nohel,John A, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *HEAT TRANSMISSION,...

The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation of a fractional trajectory, that being an average over an ensemble of stochastic trajectories. Heretofore what has been interpreted as intrinsic friction, a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. We apply the general theory developed...

Topics: DTIC Archive, UNIVERSITY OF NORTH TEXAS DENTON, *MARKOV PROCESSES, *VOLTERRA EQUATIONS, ALGORITHMS,...

This report extends the stochastic integral of Ito to allow for a certain class of anticipating integrals. Probabilistic and computational results concerning this extension are presented and iterated integrals are discussed. The motivation for this extension stems from the Ito-Volterra equation. This equation arises from feedback in the presence of white noise, and cannot be inverted using classical stochastic integrals. The inversion involving the extended integrals appears at the end of the...

Topics: DTIC Archive, Berger,Marc A, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *STOCHASTIC...

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This...

Topics: NASA Technical Reports Server (NTRS), NONLINEAR SYSTEMS, NONLINEARITY, NEURAL NETS, VOLTERRA...

The presentation begins with a brief description of the motivation and approach that has been taken for this research. This will be followed by a description of the Volterra Theory of Nonlinear Systems and the CAP-TSD code which is an aeroelastic, transonic CFD (Computational Fluid Dynamics) code. The application of the Volterra theory to a CFD model and, more specifically, to a CAP-TSD model of a rectangular wing with a NACA 0012 airfoil section will be presented.

Topics: NASA Technical Reports Server (NTRS), AERODYNAMIC CHARACTERISTICS, COMPUTATIONAL FLUID DYNAMICS,...

This paper generalizes an integral representation formula for eigenfunctions of Strum-Liouville operators, known as the Volterra transformation operator in the theory of the inverse scattering problem, to higher-order differential operators. A specific fourth-order initial value problem is considered whose solutions are expressed as an inverse-Laplace-Borel transform.

Topics: DTIC Archive, Symes,W, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER,...

A nonlinear Volterra integrodifferential equation is studied. Under various assumptions motivated by heat flow in materials with memory, results on existence of solutions are obtained, followed by various results on boundedness and the asymptotic behaviour of solutions with applications to such heat flow problems.

Topics: DTIC Archive, Londen,S -O, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *NONLINEAR...

The resolvent formula for a nonhomogeneous Volterra integrodifferential equation enables one to study the bahavior of solutions of the equation for large values of the time variable in terms of general properties of the forcing terms in the equation. This technique depends on having 'good' a priori estimates obtained for the resolvent kernel. When the solution takes its values in a Hilbert space, the resolvent kernel is a function whose values are operators on that space. It is important to...

Topics: DTIC Archive, Carr,Ralph W, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *CAUCHY PROBLEM,...

Volterra series representations of weakly nonlinear systems have been utilized in studies of both nonlinear hydrodynamics and nonlinear system identification. In the Volterra approach, the linear and nonlinear features of the system are described by the so-called linear, quadratic, cubic, etc., Volterra kernels. In the time domain these kernels correspond to the linear, quadratic, cubic, etc., impulse responses of the system, whereas, in the frequency domain they correspond to the linear,...

Topics: DTIC Archive, Powers, Edward J, TEXAS UNIV AT AUSTIN, *HYDRODYNAMICS, *SEAKEEPING, VOLTERRA...

The Nonlinear Circuit Analysis Program (NCAP) is a circuit analysis code which uses the Volterra approach to solve for the transfer functions and node voltages of nonlinear circuits. To increase the transportability, the code was written in ANSI FORTRAN. The code was revised and documented in a joint effort using both in-house and contracted manpower. This documentation is a result of that effort. The documentation is made up of three volumes: the Engineering Manual, the User's Manual, and the...

Topics: DTIC Archive, Valente ,Jon B, SYRACUSE UNIV N Y, *COMPUTER PROGRAMS, *CIRCUIT ANALYSIS, COMPUTER...

The main result of this paper is a stability theorem for a certain class of difference algorithms designed to give approximate solutions of a model inverse scattering problem in one dimension. This stability result guarantees the convergence of the approximate solutions to the exact solution of the problem as the grid of the difference scheme is refined. The results of numerical experiments are presented based on one of these schemes, in which second-order convergence is observed. Furthermore...

Topics: DTIC Archive, Symes,W W, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *INVERSE SCATTERING,...

Topics: DTIC Archive, Londen,Stig-Olof, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *PERTURBATIONS,...

The initial-value problem is studied for evolution equations in Hilbert space of the general form d/dt A(u) + B(u) not an element of f where A and B are maximal monotone operators. Existence of a solution is proved when A is a subgradient and either A is strongly-monotone or B is coercive; existence is established also in the case where A is strongly-monotone and B is subgradient. Uniqueness is proved when one of A or B is continuous self-adjoint and the sum is strictly-monotone; examples of...

Topics: DTIC Archive, DiBenedetto,Emmanuele, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *HILBERT...

This report introduces several new concepts to achieve some alleviation of the curse of dimensionality in determining the higher order kernels in a Volterra expansion. These concepts include: partitioning of the frequency scale(s), the fundamental region of formation, the diagonal strips in the two dimensional frequency space, the second- and third-order basis functions, and filtering of the measured nonlinear output to the particular frequency band under investigation. The equations for the...

Topics: DTIC Archive, NAVAL UNDERSEA WARFARE CENTER DIV NEWPORT RI, *VOLTERRA EQUATIONS, *UNDERWATER...

Topics: DTIC Archive, Londen,Stig-Olof, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *VOLTERRA...

A model reduction method for discrete bilinear systems is developed which matches q sets of Volterra and covariance parameters. These parameters are shown to represent both deterministic and stochastic attributes of the discrete bilinear system. A reduced order model which matches these q sets of parameters is defined to be a q-Volterra covariance equivalent realization (q-Volterra COVER). An algorithm is presented which constructs a class of q-Volterra COVERs parameterized by solutions to a...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, CONTROL THEORY, MATHEMATICAL MODELS,...

We consider a one-dimensional model problem for the motion of a viscoelastic material with fading memory governed by a quasilinear hyperbolic system of integrodifferential equations of Volterra type. For given Cauchy data we use the method of vanishing viscosity and techniques of compensated compactness to obtain the existence of a weak solution (in the class of bounded measurable functions) in a special case.

Topics: DTIC Archive, Nohel, J A, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *DIFFERENTIAL...

The purpose of this computer program is to compute the dynamic pressure distribution and related quantities of interest due to the diffraction of sinusoidal head waves. The method of computation is based on slender-body theory. The theoretical analysis is based on the assumption that the ship is slender. In addition, it is assumed that the incident waves are of small amplitude and their wavelength is short relative to the ship length. In the next section we shall give a brief summary of the...

Topics: DTIC Archive, Beck,Robert F, MICHIGAN UNIV ANN ARBOR DEPT OF NAVAL ARCHITECTURE AND MARINE...